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Symmetry of Information: A Closer Look

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7160)

Abstract

Symmetry of information establishes a relation between the information that x has about y (denoted I(x : y)) and the information that y has about x (denoted I(y : x)). In classical information theory, the two are exactly equal, but in algorithmical information theory, there is a small excess quantity of information that differentiates the two terms, caused by the necessity of packaging information in a way that makes it accessible to algorithms. It was shown in [Zim11] that in the case of strings with simple complexity (that is the Kolmogorov complexity of their Kolmogorov complexity is small), the relevant information can be packed in a very economical way, which leads to a tighter relation between I(x : y) and I(y : x) than the one provided in the classical symmetry-of-information theorem of Kolmogorov and Levin. We give here a simpler proof of this result.

Keywords

  • Simple Complexity
  • Chain Rule
  • Kolmogorov Complexity
  • Tight Relation
  • Universal Turing Machine

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Zimand, M. (2012). Symmetry of Information: A Closer Look. In: Dinneen, M.J., Khoussainov, B., Nies, A. (eds) Computation, Physics and Beyond. WTCS 2012. Lecture Notes in Computer Science, vol 7160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27654-5_18

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  • DOI: https://doi.org/10.1007/978-3-642-27654-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27653-8

  • Online ISBN: 978-3-642-27654-5

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